The Causal Information Bottleneck and Optimal Causal Variable Abstractions

TL;DR

This paper introduces the Causal Information Bottleneck (CIB), a causal extension of the IB method, to create interpretable variable abstractions that preserve causal control and aid causal reasoning.

Contribution

The paper proposes the CIB method, which extends the IB to causal settings, enabling the creation of causally interpretable abstractions for better causal analysis.

Findings

CIB produces causally interpretable abstractions.

CIB accurately captures causal relations.

Abstractions aid in understanding causal interactions.

Abstract

To effectively study complex causal systems, it is often useful to construct abstractions of parts of the system by discarding irrelevant details while preserving key features. The Information Bottleneck (IB) method is a widely used approach to construct variable abstractions by compressing random variables while retaining predictive power over a target variable. Traditional methods like IB are purely statistical and ignore underlying causal structures, making them ill-suited for causal tasks. We propose the Causal Information Bottleneck (CIB), a causal extension of the IB, which compresses a set of chosen variables while maintaining causal control over a target variable. This method produces abstractions of (sets of) variables which are causally interpretable, give us insight about the interactions between the abstracted variables and the target variable, and can be used when reasoning about interventions. We present experimental results demonstrating that the learned abstractions accurately capture causal relations as intended.